Problem definition

 

Table 1: Standard parameters. Note that the equations have been non-dimensionalized, leading to ``odd'' values for some parameters.

width	$-24.\leq x \leq 24.$
height	$-8.0\leq y \leq 8.0$
dx,dy	0.5,0.5
depth	1
f	$f_o + \beta y$
fo	0
$\beta$	1
g	1
horizontal viscosity	0
horizontal diffusivity	--
vertical viscosity	--
vertical diffusivity	--
bottom drag	0
dt	0.02
duration	40
equations	shallow water
forcing	none
initial conditions	see below
boundary conditions	no-slip walls

 

Initial conditions:

$$\begin{eqnarray*}u & = & \phi(x) ({{-9+6 y^2}\over{4}}) e^{-y^2/2} \\ v & = & ... ... \frac{\partial\phi}{\partial x} & = & -2B~\tanh(Bx) \; \phi ~~. \end{eqnarray*}$$

The only free parameter in the problem is the amplitude of the soliton B which should be kept smaller than 0.6 in order not to affect the accuracy of the asymptotic expansion. The value used here is B=0.395.